FSU Topology Week

Title: Spectral Radius of digraphs

Speaker: Eriko Hironaka (Florida State University)

Abstract: Certain dynamical systems, such as behavior of curves under iterations of a pseudo-Anosov mapping class on a surface, can be modeled using digraphs. In this talk we describe a deformation theory for digraphs that mimics the deformation theory of mapping classes coming from Thurston's fibered face theory. We show that the spectral radius of digraphs, after normalization, varies continuously under deformation, putting a result of Fried on pseudo-Anosov surface flows in a purely combinatorial setting.